Lyndon Law and Resign-to-Run Law

[True Federalist (진정한 연방 주의자)]

Resign to Run hilarities exist elsewhere. I know they do in Arizona (people, of course, usually decide to resign well before the GE if it's some minor office they're holding currently, say State Rep.)
I think states can't ban people from running for two federal offices at once (nevermind that technically people don't run for Vice President in the GE at all) since the Constitution does not give them the right to create additional qualifications for office.

While they probably would not be able to prevent someone running for both the Senate and the House, the wide latitude the States have in choosing Electors allows them to prevent someone for running for both the White House and the Capitol.

[True Federalist (진정한 연방 주의자)]

Is there any legal reason Ryan could not serve in the House and as VP at the same time?

Yes.

Article I Section 6 Clause 2
No Senator or Representative shall, during the Time for which he was elected, be appointed to any civil Office under the Authority of the United States which shall have been created, or the Emoluments whereof shall have been increased during such time; and no Person holding any Office under the United States, shall be a Member of either House during his Continuance in Office.

This is also why we don't have members of Congress serving as Secretary of State or the like.

[True Federalist (진정한 연방 주의자)]

Why is VP considered an Office?

Consider Article II Section 4:
The President, Vice President and all civil Officers of the United States, shall be removed from Office on Impeachment for, and Conviction of, Treason, Bribery, or other high Crimes and Misdemeanors.

There is also the precedent established by John C. Calhoun.  He resigned the Vice-Presidency over two months early to accept being selected as Senator from South Carolina.